The morphemic status of -id can be proved by its regular occurrence in Modern English adjectives (mostly of Roman origin): horrid, stupid, rapid, acid, sordid, valid, solid, etc.
I would suggest that it only makes sense to call something a "suffix" if either it is productive (i.e. you can use it to create new words from existing ones), or if the words in which it exists are envisaged by native speakers of being made of a smaller element plus that suffix.
In the case of -id, it's not clear to me that either of these are the case. If you can think of cases where you could create a plausible new word by adding -id to an existing one, or if you really think that speakers envisage, say, "stupid" as being made of the morpheme "stup(or)" plus -id, then you might want to call it a suffix. I personally don't think that either of these conditions are true.
[In Latin, "stupor" could mean what in English would now be "stupidity"-- i.e. to a Latin speaker, there was arguably a sense that "stupidus" was derived from a "suffix" -idus, but I don't think that today English speakers see "stupid" as being derived from "stupor" even though both words have been borrowed; and "solidus" possibly derived from e.g. "solum" (="base", "floor"), or at least they share a common derivation, but this notion is lost in English today, as indeed the relationship between Spanish "sólido"~"suelo" or French "solide"~"sol" has probably also been lost.]
The NOAD describes -id as suffix used to form adjectives (such as putrid and torrid) or form nouns (such as chrysalid and pyramid).
In the first case, its origin is from Latin -idus; in the latter case, its origin is from Latin -idis, which derives from the Greek -is, -id-.
Wiktionary describes the suffix with "appended to various foreign words to make an English adjective form" and "often added to words of Greek, sometimes Latin, origin."
The words you reported derives from Latin words that end in idus (horridus, stupidus, rapidus, acidus, sordidus, validus, solidus), but I would not see valid as val + id.